A fluid can generally be classified as ideal, Newtonian or non-Newtonian based on the behavior of the fluid under shear stress. An ideal fluid has no shear stress in a flow field and its viscosity is zero. No fluids which exhibit this type of behavior exist. In a Newtonian fluid, such as water, glycerol, the shear stress is directly proportional to the shear rate; and its viscosity is independent of the shear rate. In a non-Newtonian fluid, the shear stress is dependent on the shear rate and its viscosity may vary with the shear rate in a complex manner. See FIG. 1.
Viscosity is a measurement of the behavior of a fluid under stress. It is, therefore, important to be able to accurately determine the viscosity of a fluid in order to improve the design of pumps, stirrers, mixers, liquid transport devices, and reactors. Futhermore, the molecular weight of a polymer solution is related to its viscosity at zero shear rate and an accurate determination of the zero shear rate viscosity of a polymer solution enables one to obtain an accurate measurement of its molecular weight.
The viscosity of a fluid, .eta. is defined as the force in dynes per square centimeter (cm.) necessary to maintain a velocity of 1 cm. per second (sec.) between two layers of a fluid 1 cm. apart. Many methods have been developed to determine the viscosity of fluids. The earliest is the capillary tube viscometer. For a capillary tube viscometer, viscosity may be defined as: ##EQU1## where v is volume in cc., t is time in sec., r is the radius in cm. of a narrow tube through which the fluid is flowing, L is the length in cm: and p is the pressure drop between length L in dynes per sq. cm.
Although this method can be used to determine the viscosity of Newtonian and non-Newtonian fluids, this suffers from many disadvantages. It is difficult to accurately measure the small pressure differences involved, precisely calibrate the diameter of the capillary tube and keep the capillary tube clean. Further, the capillary tube viscometer is only applicable for determining the viscosity at high shear rates. It cannot be used to determine viscosity at low shear rates.
Another approach is the falling sphere or falling ball viscometry first described in G.G. Stokes, Camb. Phil. Trans., 9, p.8 (1851). In this method, the time, t sec., taken for a sphere d to fall through a predetermined distance L cm. in an infinite fluid medium is measured. The viscosity is then calculated in accordance with the following equation: ##EQU2##
However, in the falling sphere method, the following assumptions are made: the spheres are falling in an infinite medium, the density of the falling sphere is in a suitable range for the equation to hold true, and the sphere must be perfectly round, so that it will fall vertically through the fluid and will not veer in one direction or another or fall erratically.
In practice, spheres can only be made from a limited range of materials, such as, glass, aluminum or steel and the density cannot be adjusted. Further, very few spheres are truly round and, as a consequence, the fall through the fluid medium is not truly vertical. Moreover, a fluid must be held in a container, therefore, wall effects have to be considered. Thus, inaccuracies arise from the non-vertical fall of a sphere and a correction factor for wall effects must be applied.
Moreover, the falling sphere method does not provide an exact solution for non -Newtonian fluids because of the geometric complexities involved.
Falling cylinder and falling plunger viscometers have also been designed. See, Lohrentz, et al., A. I. Ch. E. Journal, 6, No. 4 p. 547-549 (1960) and G. S. Smith, J. Inst. Pet., 43, p. 227-230 (1957). These are found wanting because it is difficult to construct the falling cylinder or plunger, difficult to obtain cylinders or plungers with different densities and difficult to maintain a vertical fall through the fluid. To maintain a vertical fall through the fluid, guide pins or bushings are required. Further, the eccentricity effect is very significant. Because of these problems, it is difficult to account for the systematic error in viscosity measurement by the falling cylinder or plunger method.
A rotating cylinder viscometer with two coaxial cylinders, a rotating outside cylinder.and a stationary inside cylinder had been developed to measure the viscosity of non-Newtonian fluids. See Van Wazer et al., Viscosity and Flow Measurement, p. 47-96, Interscience Publishers, New York, 1963. However, the rotating cylinder viscometer is difficult and expensive to make. Further, it is very difficult to maintain a constant temperature in the system and evaporation of the fluid from the open-mouth container is unavoidable. These difficulties translate into unacceptably large errors in the viscosity obtained.
It is, therefore, an objective of the present invention to develop an apparatus and a method to determine accurately the viscosity of Newtonian and non-Newtonian fluids with the smallest systematic error possible.
It is a further objective to develop an apparatus and method which is inexpensive to manufacture and easy to use.